In Italy public transport is very extensive and is present in any region. In particular, it is possible to move around almost every city using the national railway service known as Trenitalia, which also has a bus service. We strongly recommend using one of these two services because in Italy taxi prices are really high and not all cities have an Uber service!
By downloading the Trenitalia app it will be possible to access dozens of offers on travel (such as 2x1 tickets or discounts with the insertion of a code) as well as to speed up the purchase of tickets that will be in digital format. The difference between the various trains in Italy, however, is very clear: there are those at high speed and there are regional.
Regionals are slower and make more stops, but they are also the ones that cost less. The general advice is also to take the trains that travel at night, since they are the trains with the lowest costs ever.
The high speed (AV) is however very convenient in quality and price ratio, for this reason we recommend to take a look from the application.
As for buses, these always depend on Trenitalia but there are many other companies that deal with driving even for long routes. Some Italian cities are small medieval villages, and it is therefore almost impossible to reach them by train given the lack of tracks.
Bus tickets can be purchased online and applications... but also from tobacco shops! In the classic Italian "tabaccheria", in fact, you can buy tickets of any type and pay in cash or by card.
However, these are closed on Sundays, so you should always buy them from Monday to Friday, or Saturday morning.
There are many low cost companies, such as Flixbus or Itabus... with a few euros, you can visit the most beautiful Italian cities.